Here, \(S\)  is the scalar factor that appears in the double copy relation
(REF ), which we fixOur procedure to fix \(S\)  closely follows the treatment for type N spacetimes in [1]},
which also finds a set of first order differential equations for \(S\)  that are integrable. This approach differs
slightly from the one used for type D spacetimes in [2]}, which relies on prior work showing how the
double, single and zeroth copies can all be written in terms of a single Killing spinor that always exists in type D.
by requiring that \(F_{\mu \nu } =\frac{1}{8} f_{AB} \sigma ^{AB}_{\mu \nu }\)  satisfy Maxwell's equations on the
Kerr-NUT-(A)dS background.
